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Long Range Internal Stresses


TEM Micrograph
TEM Micrograph of single crystal copper deformed along the [100] direction
Backstresses or long range internal stresses (LRIS) exist in plastically deformed crystalline materials. These backstresses are a fundamental mechanical property related to plastic deformation. Single crystal Cu deformed along the [100] axis develops a heterogeneous dislocation microstructure which is known to produce such LRIS. This microstructure acts as a composite material with hard dislocation dense walls, and soft dislocation free interiors.

Advanced Photon Source Beamline 34-ID Monochromatic X-ray Microbeam, focused using two sets of Baez-Kirkpatrick Mirrors

Argonne National Labs –
Advanced Photon Source
Beamline 34-ID
Monochromatic X-ray Microbeam, focused using two sets of Baez-Kirkpatrick Mirrors

Differential Aperature X-Ray Microscopy

microbeamThe dislocation microstructure contains numerous dislocation cells with different crystallographic orientations and elastic strains, only part of the sample is illuminated by the monochromatic X- ray beam and will diffract. The photon energy is therefore scanned over a large enough energy range to extract diffraction data from the probed sample volume. Depth resolution is provided by incrementally translating a Pt wire parallel to the sample surface (for each energy) and using triangulation to determine the sample depth from which the observed diffracted X-ray intensity originates.

 Using the DAXM technique we’re able to measure internal stresses present in our deformed samples. Currently we’re working on obtaining entire strain tensors from the microstructure, to develop a full picture of the stress states. Statistical models are being developed for the stress distributions, and underlying causes are being identified. TEM and computer simulations are also being performed to supplement current findings.



 We now have developed a technique that can assess the full strain tensor such as in Equal Channel Angular Pressing (ECAP).








Harper-Dorn Creep

Creep is referred to as the permanent deformation at stresses usually smaller than the yield strength. Creep is a diffusion controlled phenomenon, hence it becomes important only at high temperatures (>0.5 Tm where Tm is the melting temperature). Stress exponent, activation energy and dislocation density are a few of the signatures of a creep mechanism.

Creep occurring at very low stresses (<10-4 – 10-6G, where G is the shear modulus) and at very high temperatures (>0.9Tm) belongs to the Harper – Dorn creep regime. Conventionally, Harper-Dorn creep is identified with a stress exponent of 1, activation energy equal to volume diffusion and stress independent dislocation density. As shown in the figure, stress exponent value in the Harper – Dorn regime is controversial!

Solving the controversy: We’re making new insights into this 50 year old problem, which is important in understanding a few industrial processes and geological phenomenon (e.g. in glacier flow, geodesic plate movement, etc)


Single crystalline samples free from grain boundary effects Ultrahigh purity (99.999%)
Low purity samples do not show deviation from 5-power law creep in the Harper-Dorn regime
Non-contact laser based extensometer
Contact based extensometers, e.g. LVDT may exert enough friction to influence the applied very low stresses
High strains attained in tests to achieve steady state
Many of the studies reporting conventional Harper-Dorn creep failed to reach steady state
Constant load as well as load cycling tests
No difference in results between the two kinds of loading procedures
Large sized samples (diameter = 24mm) as well as small samples (diameter = 7mm)
No size dependence observed




The creep behavior in the Harper-Dorn creep regime was identified with a stress exponent closer to n ≈ 3 rather than the conventional value of n = 1. When plotted as the steady-state creep rate against the normalized stress on logarithmic axes, the present results are in good agreement with most of the earlier experimental data for high purity aluminum along with the early results of Harper and Dorn when their data is plotted without including a threshold stress. The dislocation densities measured within this low stress region are consistent with the behavior anticipated from a direct extrapolation of similar dislocation density data recorded in the conventional power-law region at high stresses. The activation energy is the same as the activation energy for the lattice diffusion. A dislocation network model can accurately capture the deformation behavior in the Harper-Dorn creep regime.


Additive Manufacturing

We are characterizing the elevated temperature creep properties of additively manufactured (AM) Inconel. There is an interest in assessing the ductility, strength, and fatigue behavior of the alloy under stress.


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